Let H and A be the hamiltonian, resp. the modular operator associated with an invariant faithful normal state ω of a W*-dynamical system (A, α). Then Δ = f(h) for some decreasing function f if and only if (roughly speaking) ω is 2-passive with respect to α. It follows that under certain conditions a 3-passive state is an equilibrium (i.e. KMS) state.
Cite this article
J. de Cannière, Functional Dependence between the Hamiltonian and the Modular Operator Associated with a Faithful Invariant State of a <i>W</i>*-Dynamical System. Publ. Res. Inst. Math. Sci. 20 (1984), no. 1, pp. 79–96